Inclusion Criteria:
1. Males or females, age 18 years or older
2. Diagnosis of multiple myeloma (MM) and documentation of treatment
* ARM 1: Must have prior exposure to an immunomodulatory drug (IMiD) and proteasome inhibitor (PI) and have had 2 prior regimens/lines of therapy; but there is no maximum number of prior regimens, and prior autologous bone marrow transplant is acceptable if \> 12 weeks from transplantation; patients may have received prior carfilzomib (sensitive, relapsed and refractory \[having progressed while receiving carfilzomib or within 60 days of stopping carfilzomib\] are all eligible), but must be \> 4 weeks from last dosing of carfilzomib
* ARM 2: Must have had at least 1 but no more than 3 prior lines of anti-myeloma therapy; may be refractory to lenalidomide but sensitive to carfilzomib; prior exposure to carfilzomib is allowed but may not be refractory to carfilzomib; subjects must be \>= 8 weeks from last carfilzomib therapy
* A line of therapy is defined as a course of therapy that is not interrupted by progressive disease; for example, induction therapy, autologous stem cell transplantation, and maintenance therapy without intervening progressive disease is one line of therapy
3. Confirmed evidence of relapse/disease progression from immediately prior MM therapy or relapsed and refractory to the immediately prior treatment; relapsed and refractory disease is defined as those who are non-responsive (\< minimal response) on salvage therapy or experience disease progression within 60 days of last therapy in patients who have achieved an MR or better to previous therapy; relapsed disease is defined as previously treated myeloma that progresses and requires the initiation of salvage therapy but does not meet IMWG criteria for relapsed and refractory
4. Patients may have received prior carfilzomib (sensitive, relapsed and refractory all eligible); response and duration of prior carfilzomib therapy must be known
5. Patients must have measurable disease defined as at least one of the following:
* Serum M-protein \>= 0.5 g/dl (\>= 5 g/l)
* Urine M-protein \>= 200 mg/24 hours (h)
* Serum free light chain (FLC) assay: involved FLC level \>= 10 mg/dl (\>= 100 mg/l) and an abnormal serum free light chain ratio (\< 0.26 or \> 1.65)
* Quantitative immunoglobulin \> 500mg/dL for Immunoglobulin A (IgA) or \> 500mg/L for Immunoglobulin D (IgD), only for IgA and IgD myeloma (by nephelometry) when the protein electrophoresis under-represents disease burden
* Biopsy proven plasmacytoma \> 1x1 cm (should be measured within 28 days prior to initial investigational agent dosing)
6. Subject has an Eastern Cooperative Oncology Group (ECOG) =\< 2 performance status OR Karnofsky \>= 60% performance status
7. Females of childbearing potential (FCBP)
* A female of childbearing potential is a sexually mature woman who: 1) has not undergone a hysterectomy or bilateral oophorectomy; or 2) has not been naturally postmenopausal for at least 24 consecutive months
* Females of childbearing potential must have a negative serum beta-human chorionic gonadotropin (beta-hCG) pregnancy test with a sensitivity of at least 50 milli-international units per milliliter(mIU/mL), within 10-14 days of study start (during screening)
* FCBP must also agree to ongoing pregnancy testing. Pregnancy testing is not required for post-menopausal or surgically sterilized women
* Females must agree to avoid pregnancy during the study and must agree to use a medically acceptable method of birth control as determined by the study doctor while participating in the study and for at least 5 months after the last dose of study medication
8. Men must agree to use contraception (i.e. a latex condom) during sexual contact with a FCBP even if they have had a successful vasectomy and agree to not donate sperm for 5 months after last study therapy (SAR650984, lenalidomide and carfilzomib).
9. Voluntary written informed consent before performance of any study-related procedure not part of routine medical care with the understanding that consent may be withdrawn by the subject at any time without prejudice to future medical care
10. Ability to understand the purpose and risks of the study and provide signed and dated informed consent and authorization to use protected health information (in accordance with national and local subject privacy regulations)
11. For patients with platelets \> 100,000 cells/ul (100x10\^9/L) able to take aspirin daily as prophylactic anticoagulation therapy for ARM 2 (patients intolerant to aspirin may use warfarin, low-molecular-weight heparin or equivalent anti-platelet therapy)
12. Inclusion Clinical Laboratories Criteria. The following laboratory results must be met:
* Absolute neutrophil count (ANC) \> 1,000 cells/dL (1.0 x 10e9/L) (growth factor cannot be used within the previous 7 days)
* Hemoglobin \>= 8.0 g/dl (without transfusion within the previous 7 days)
* Platelet count \> 75,000 cells/dL (75 x 10e9/L)
* Creatinine clearance \>= 30 mL/min (Cockcroft-Gault equation)
* Serum glutamic oxaloacetic transaminase (SGOT)/aspartate aminotransferase (AST) or serum glutamate pyruvate transaminase (SGPT)/alanine aminotransferase (ALT) \< 2.5 x upper limit of normal (ULN)
* Total bilirubin =\< 1.5 x ULN (excluding Gilbert's)
* Serum calcium (corrected for albumin) level at or below the ULN range (treatment of hypercalcemia is allowed and subject may enroll if hypercalcemia returns to normal with standard treatment) prior to study therapy initiation
* Left ventricular ejection fraction (LVEF) \>= 40% (by echocardiogram or multigated acquisition scan (MUGA) testing)
* Fasting glucose under control (\< 150 mg/dL \[8.3 mmol/L\])
Exclusion Criteria:
Patients who have met all the inclusion criteria listed above will be screened for the following exclusion criteria:
1. Diagnosed or treated for another malignancy within 3 years of enrollment, with the exception of complete resection of basal cell carcinoma or squamous cell carcinoma of the skin, an in situ malignancy, low-risk prostate cancer after curative therapy or complete resection of other advanced malignancy with the expectation that the patient has received curative therapy
2. Patient has received other investigational drugs with 21 days before enrollment (or must be \> than four half-lives of the experimental agent); no prior SAR650984 anti-CD38 antibody therapy allowed
3. History of significant cardiovascular disease unless the disease is well-controlled or history of myocardial infarction in the past 6 months; significant cardiac diseases includes second/third degree heart block; significant conduction abnormalities, significant ischemic heart disease; poorly controlled hypertension; congestive heart failure of New York Heart Association (NYHA) class II or worse (slight limitation of physical activity; comfortable at rest, but ordinary physical activity results in fatigue, palpitation, or dyspnea) and inability to tolerate intravenous hydration necessary for study therapy administration
4. Prior autologous or allogeneic peripheral stem cell transplant within 12 weeks of the first dose of study treatment
5. Daily requirement for corticosteroids (\> 10 mg prednisone once daily (QD) or equivalent)
6. Patients with evidence of significant mucosal or internal bleeding
7. Prior radiation therapy or chemotherapy within 2 weeks or major surgical procedure within 4 weeks of the first dose of study treatment
8. Known active infection requiring parenteral or oral anti-infective treatment, once a patient has completed antibiotics and symptoms of infection have resolved to \< grade 2, they are then considered eligible from an infection standpoint
9. Serious psychiatric illness, active alcoholism, or drug addiction that may hinder or confuse follow-up evaluation
10. Any medical conditions that, in the Investigator's opinion, would impose excessive risk to the patient; examples of such conditions include any pre-existing kidney disease (acute or chronic, unless renal insufficiency is felt to be secondary to MM), hypertension, active seizure disorder or pulmonary diseases that would impose excessive risk to the patient
11. Patient has hypersensitivity to boron, mannitol sucrose, histidine (as base and hydrochloride salt) and polysorbate 80 or any of the components of study therapy including required prophylactic medications
12. Known human immunodeficiency virus (HIV) seropositivity or active hepatitis B or C viral infection
13. Neuropathy \>= grade 3 or painful neuropathy \>= grade 2 (National Cancer Institute Common Terminology Criteria for Adverse Events \[NCI CTCAE\] version \[v\]4.03)
14. Gastro-intestinal abnormalities, including bowel obstruction, inability to take oral medication, requirement for intravenous (IV) alimentation, active peptic ulcer or prior surgical procedures or bowel resection affecting absorption
